Monday, January 14, 2013

Thinking Blocks and the Common Core

Thinking Blocks is an online problem solving tool that enables students to build physical models of math word problems. Using brightly
colored blocks, students represent mathematical relationships and identify
known and unknown quantities.The model provides students with a
powerful image that organizes information and simplifies the problem
solving process.By
modeling increasingly complex word problems, students develop strong
reasoning skills which will facilitate the transition from arithmetic to
algebra.

Thinking Blocks programs include word problems involvingaddition and subtraction, multiplication and division, fractions, and ratio and proportion. Within each of the four main modules, there are both simple and multi-step word problems for students to solve. These problem sets refer togeneralized visual models that can be applied to a variety of scenarios. While results are not stored from session to session, each student's progress can be monitored during a single practice period.

Thinking Blocks supportsmany of the common core state standards for mathematics, particularly those found in grades 1 through 6. The standards described below come directlyfrom the Common Core website.

Grade 1 Thinking Blocks Addition and Subtraction Module

1.0A.1: Use
addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart,
and comparing, with unknowns in all positions, e.g., by using objects,
drawings, and equations with a symbol for the unknown number to
represent the problem.

1.0A.2: Solve
word problems that call for addition of three whole numbers whose sum
is less than or equal to 20, e.g., by using objects, drawings, and
equations with a symbol for the unknown number to represent the
problem.

Grade 2 Thinking Blocks Addition and Subtraction Module

2.0A.1: Use
addition and subtraction within 100 to solve one- and two-step word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all positions,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem.

Grade 3Thinking Blocks Multiplication and Division Module

3.0A.1: Use
multiplication and division within 100 to solve word problems in
situations involving equal groups, arrays, and measurement quantities,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem.

3.0A.8: Solve
two-step word problems using the four operations. Represent these
problems using equations with a letter standing for the unknown
quantity. Assess the reasonableness of answers using mental computation
and estimation strategies including rounding.

Grade 4 Thinking Blocks Multiplication/Division and Fraction Modules

4.0A.3: Solve multi-step word
problems posed with whole numbers and having whole-number answers
using the four operations, including problems in which remainders must
be interpreted. Represent these problems using equations with a
letter standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies including
rounding.

4.NF.3: Solve word problems
involving addition and subtraction of fractions referring to the same
whole and having like denominators, e.g., by using visual fraction
models and equations to represent the problem.

4.NF.4: Solve word problems
involving multiplication of a fraction by a whole number, e.g., by
using visual fraction models and equations to represent the problem.

Grade 5 Thinking Blocks Fraction Module

5.NF.2: Solve
word problems involving addition and subtraction of fractions
referring to the same whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations to represent the
problem. Use benchmark fractions and number sense of fractions to
estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

5.NF.7: Solve
real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g.,
by using visual fraction models and equations to represent the
problem. For example, how much chocolate will each person get if 3
people share 1/2 lb of chocolate equally? How many 1/3-cup servings are
in 2 cups of raisins?

Grade 6Thinking Blocks Ratio and Proportion Module6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For
example, “The ratio of wings to beaks in the bird house at the zoo
was 2:1, because for every 2 wings there was 1 beak.” “For every vote
candidate A received, candidate C received nearly three votes.”

6.RP.2: Understand the
concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and
use rate language in the context of a ratio relationship. For
example, “This recipe has a ratio of 3 cups of flour to 4 cups of
sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid
$75 for 15 hamburgers, which is a rate of $5 per hamburger.”

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About the Author

Colleen King is a math educator with 15 years experience working with K-12 students in a variety of settings. Colleen publishes MathPlayground.com and develops math games, teaching tools, and learning resources that are used in classrooms throughout the world. She has presented her work at ISTE and NCTM conferences and has co-authored several teaching articles.